Question: What number makes this equation true?
Solution: ${?}+261=630$ ${261}$ ${630}$ $+?$ Let's start by adding hundreds to ${261}$ until we get as close to ${630}$ as possible without going over ${630}$. $\begin{aligned} {261} +100}=361\\\\ {361} +100}=461\\\\ {461} +100}=561 \end{aligned}$ If we add $3 \text{ hundreds}}$, or $300}$, we reach $561$. We cannot add anymore hundreds without going over ${630}$. ${261}$ ${630}$ ${561}$ $+300$ Next, let's add tens to $561$ until we get as close to ${630}$ as possible without going over ${630}$. $\begin{aligned} 561 +{10}=571\\\\ {571} +{10}=581\\\\ {581} +{10}=591\\\\ {591} +{10}=601\\\\ {601} +{10}=611\\\\ {611} +{10}=621 \end{aligned}$ If we add ${6 \text{ tens}}$, or ${60}$, we reach $621$. We cannot add anymore tens without going over ${630}$. ${261}$ ${630}$ ${561}$ ${621}$ $+300$ $+60$ Finally, how many ones should we add to $621$ to get to ${630}?$ $621+{9}={630}$ ${261}$ ${630}$ ${561}$ ${621}$ $+300$ $+60$ $+9$ We added $3 \text{ hundreds}}$, ${6 \text{ tens}}$, and ${9\text{ ones}}$ to ${261}$ to get to ${630}$. $300}+{60}+{9}={369}$ ${261}$ ${630}$ ${561}$ ${621}$ $+300$ $+60$ $+9$ $+369$ ${369}+261=630$